They just couldn’t get it to work very well, and realised that getting things working was more or less a lost cause. It took years to get Flash play nice on the desktop, and it still doesn’t actually work all that well on actual computers, which have significantly more resources to spare than mobile devices. The blame for this is not entirely on Adobe, though – in my experience a large portion of Flash-based content on the web has been implemented poorly and hence tax even computers to the extreme to run. This type of Flash apps are just impossible to get running on the mobile. Additionally, content providers didn’t seem to care jack squat about optimising content for the mobile, and providing a good user experience on a site that runs poorly encoded 1080P video through Flash is just impossible on the current generation of devices (and probably the next couple gens as well), leading to embarrassing video demos of the Flash player sucking at video playback.

Web-based mobile app discovery doesn’t work very well. People expect to get their apps from the App Store or the Android Market. Despite a lot of effort being put onto smooth web app installation on mobile, it just doesn’t work the same as native apps. As a result, the demand for Flash browser plugin on mobile was significantly less than the demand for good tools for creating apps distributable though the channels supported by Apple and Google.

So, someone Adobe just did the math and decided to drop developing an effort that didn’t have much actual demand from Adobe’s customers (you know, the developers) and which was going nowhere.